Topological origins of bound states in the continuum for systems with conical intersections

Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 90, 013001 (2003)]. It was also found that these states are destroyed within the Born-Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original two-dimensional two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove the GP within a two-state problem. Using the stabilization graph technique we shown that the GP is crucial for emergence of BSCs.